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Langmuir 1997, 13, 1010-1015
Heterogeneity of Pillared Clays Determined by Adsorption of SF6 at Temperatures Near Ambient† Jacek Jagiełło,‡ Teresa J. Bandosz, and James A. Schwarz* Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, New York 13244-1190 Received November 16, 1995. In Final Form: February 9, 1996X Pillared clays are studied using sulfur hexafluoride adsorption isotherms measured at temperatures near ambient over the pressure range 1-760 Torr. Under these conditions the adsorption takes place predominantly in micropores due to their enhanced adsorption potential. Data are analyzed using the stable numerical method for solving the adsorption integral equation. The adsorption energy distributions (AEDs), which characterize energetic heterogeneity of adsorbate-adsorbent interactions, are derived. It is assumed that the AED is determined by the microstructure of the clay material and the pore width is calculated. In the discussion of the adsorption energetics the effects of pore sizes, density of mineral layers, and the interaction of adsorbed molecules with pillars are considered. The results obtained from the analysis of adsorption data and XRD analysis are consistent. The difficulties in evaluation of pore size distribution due to the sensitivity of the assumed structural model are discussed.
Introduction Pillared clays are a group of materials that can be used as catalysts, catalyst supports,1-4 media for gas storage and separation,5 and media for removal of heavy metals from the environment.6 A knowledge of their basic sorption and structural characteristic is an important factor that determines and limits their applications. The structure and surface properties of these materials have been studied by physical and chemical methods such as X-ray diffraction, FTIR, NMR, potentiometric titration, inverse gas chromatography, and physical adsorption.1-12 Physical adsorption methods are of particular interest. They not only can be used to obtain basic structural characteristics such as surface area and porosity but also may provide direct insight of material microstructure. Adsorption data were recently used to characterize the microstructure of pillared clays in terms of their micropore size distributions (PSDs).5,10-13 The PSDs were calculated using the Horvath-Kawazoe14 and the Jaroniec-Choma15 methods as well as a combination of the two.10 In these calculations the slit-shape model of pores was assumed. * Author to whom correspondence should be addressed. † Presented at the Second International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland/Slovakia, September 4-10, 1995. ‡ Permanent address: Faculty of Fuels and Energy, University of Mining and Metallurgy, 30-059 Krako´w, Poland. X Abstract published in Advance ACS Abstracts, September 15, 1996. (1) Occelli, M. L.; Tindwa, P. M. Clays Clay Miner. 1983, 31, 22. (2) Pinnavaia, T. J. Science 1983, 220, 365. (3) Suib, L.; Tanguay, I.; Occelli, M. L. J. Am. Chem. Soc. 1986, 108, 6972. (4) Auer, H.; Hoffmann, H. Appl. Catal. 1993, 97, 23. (5) Yang, R. T.; Baksh, M. S. A. AIChE J. 1991, 37, 679. (6) Bergaoui, L.; Lambert, J.-F.; Suquet, H.; Che, M. J. Phys. Chem. 1995, 99, 2155. (7) Bandosz, T. J.; Jagiełło, J.; Putyera, K.; Schwarz, J. A. J. Chem. Soc., Faraday Trans. 1994, 90, 3573. (8) Bandosz, T. J.; Jagiełło, J.; Schwarz, J. A. J. Phys. Chem. 1995, 99, 13522. (9) Bandosz, T. J.; Jagiełło, J.; Andersen, B.; Schwarz, J. A. Clays Clay Miner. 1992, 40, 306. (10) Baksh, M. S. A.; Yang, R. T. AIChE J. 1992, 38, 1357. (11) Gil, A.; Montes, M. Langmuir 1994, 10, 291. (12) Gil, A.; Guiu, G.; Grange, P.; Montes, M. J. Phys. Chem. 1995, 99, 301. (13) Baksh, M. S.; Kikkinides, E. S.; Yang, R. T. Ind. Eng. Chem. Res. 1992, 31, 2181. (14) Horvath, G.; Kawazoe, K. J. Chem. Eng. Jpn. 1983, 16, 470. (15) Jaroniec, M.; Choma, J. Mater. Chem. Phys. 1986, 15, 1521.
S0743-7463(95)01040-7 CCC: $14.00
The objective of the present paper is to investigate the relationship between adsorption characteristics and microstructure of pillared clay. The adsorption energy distributions (AEDs) which characterize energetic heterogeneity of adsorbate-adsorbent interactions are derived from sulfur hexafluoride adsorption isotherms measured at temperatures near ambient over the pressure range 1-760 Torr. Under these conditions, which are far from condensation for SF6 (saturation pressure ≈ 50 atm), the adsorption takes place predominantly in micropores due to their enhanced adsorption potential. The practical advantages of such experimental conditions compared with conventional nitrogen isotherms at 77 K are that high vacuum is not required and it is relatively easy to perform measurement at various temperatures. In our analysis of the adsorption data we assume that the AED is governed by the microstructure of the clay material. In our discussion of adsorption energetics, we consider effects of pore sizes, density of mineral layers, and interactions of adsorbed molecules with pillars. We find good agreement between pore sizes derived from XRD and from our analysis of adsorption data. We also point out difficulties in evaluation of PSDs for materials of unknown structure due to the sensitivity of the calculated PSD on the assumed structural model. Experimental Section Materials. The Wyoming bentonite (Black Hill) was mixed with solutions of Chlorhydrol to intercalate large polycations into the mineral interlayer space. Chlorhydrol is the trade name of a solution of hydroxyaluminum cations manufactured by Reheis Chemical Company. The intercalation was done according to the method described elsewhere.16 The resulting product was washed with distilled water until the reaction to chloride ions was negative. The sample obtained was designated as W-A. To induce changes in the pore structure of the intercalated sample, the material was heat treated at 673 and 873 K for 10 h. The samples obtained in this way are designated as W-A(673) and W-A(873), respectively. Heat treatment caused the dehydration and dehydroxylation of pillars accompanied by the shrinking of the interlayer distance.2,9,17 Methods. X-ray Diffraction Analysis. Oriented clay mounts were made by settling a suspension of bentonite onto a glass slide. All clay mounts were dried at room temperature and heat(16) Fahley, D. R.; Williams, K. A.; Harris, J. R.; Stapp, P. R. U.S. Pat. 4,845,066, 1989. (17) Bandosz, T. J.; Gomez-Salazar, S.; Putyera, K.; Schwarz, J. A. Microporous Mater. 1994, 3, 177.
© 1997 American Chemical Society
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treated clay mounts were rehydrated after calcination at 673 K. X-ray diffractograms were produced with Philips PW1729 diffractometer using filtered Cu KR radiation. Volumetric Sorption Experiments. Adsorption isotherms were measured by a GEMINI III 2375 surface area analyzer (Micromeritics). Before the experiment the samples were heated for 10 h at 473 K and then outgassed at this temperature under a vacuum of 10-2 mmHg. Sulfur hexafluoride adsorption isotherms were measured for each sample at three different temperatures around ambient (266-298 K), which was accomplished with a home made thermostated system controlled by a Fisher Scientific Isotemp refrigerated circulator, Model 900. Nitrogen adsorption isotherms were measured at 77 K.
Analysis of Adsorption Data Adsorption Energy Heterogeneity. The quantitative description of adsorption energy heterogeneity is usually given by the adsorption energy distribution (AED). The AED characterizes the adsorbate-adsorbent system and may be evaluated from the experimental adsorption isotherm, v. The relationship between v and the unknown AED, χ, is given by the integral equation
v(p,T) )
∫Rβ θ(p,T,q) χ(q) dq
(1)
where p and T are the experimental pressure and temperature and θ(p,T,q) is the so-called local adsorption isotherm which describes adsorption on surface sites having adsorption energy q. The total number of adsorption sites, v0, is given by
v0 )
∫Rβ χ(q) dq
(2)
The function θ is the kernel of the integral equation and its mathematical form represents the accepted model of adsorption. In our analysis we accept the FowlerGuggenheim (FG) adsorption isotherm18 representing the monolayer localized adsorption model and we assume the random topography of adsorption sites which lead to the following expression for θ19
[
θ(p,T,q) ) 1 +
(
)]
ωv/v0 + q K exp p RT
-1
(3)
where K is the pre-exponential factor of Henry’s law constant and ω is a parameter related to the energy of interaction between adsorbate molecules. Our choice of the model for adsorption in pillared clays is based on their known structural features. The space between the montmorillonite layers creating a slit-shaped pore may accommodate up to two adsorbate molecules in width which means that we deal with monolayer adsorption on each wall of the pore. The pillars between the montmorillonite layers will divide the adsorption space into partially closed microcavities which will tend to immobilize adsorbate molecules. In addition, the topography of sites in such a structure is considered random since neighboring sites in each cavity have different adsorption energies according to their positions in a cavity. To solve eq 1 with respect to χ(q) we apply a numerical method, SAIEUS, described elsewhere.20 The AED, χ(q), is represented in this method by a linear combination of (18) Fowler, R. H.; Guggenheim, E. A. Statistical Thermodynamics; Cambridge University Press: Cambridge, 1949. (19) Rudzin´ski, W.; Jagiełło, J.; Grillet, Y. J. Colloid Interface Sci. 1982, 87, 478. (20) Jagiełło, J. Langmuir 1994, 10, 2778-2785.
the B-spline functions21 with equally spaced knots in the range of (R, β). The problem is solved using regularization combined with non-negativity constraints. The degree of regularization/smoothing is controlled by the so-called smoothing parameter λ. In this method the choice of λ is based on the analysis of a measure of the effective bias introduced by the regularization procedure and a measure of uncertainty of the solution. Such an approach ensures that we extract maximum available information from the data but avoid introducing artifacts. Relationship between Pore Size and Energy of Adsorption. It was proposed by Everett and Powl22 that one can evaluate micropore sizes of carbons with uniform pore structure using adsorption data measured in Henry’s law region and adsorption potentials calculated for model micropores. This approach was later extended23,24 for the analysis of adsorption data measured over a broader ranges of pressure on heterogeneous carbons. The basic assumption in this approach is that the energy of adsorption in micropores is determined by their sizes. The relationship between the pore size, x, and the adsorption energy, q, defined by the well depth, up*, of the gas-solid interaction potential
q(x) ) up*(x)
(4)
is based on the assumed pore model. Using function q(x) and the calculated AED, one can evaluate the pore size distribution (PSD), φ(x), from the relationship
φ(x) ) χ(q)
∂q ∂x
(5)
Here we apply the same general approach to pillared clays assuming the slitlike model for the shape of their pores. The potential, up, of interaction between a gas molecule and a pore is given in this case as a sum of potentials, us, of gas-solid interactions with single walls
up(z) ) us(z) + us(x - z)
(6)
where z is the distance of the molecule from the surface atoms nuclei of one of the pore walls which are separated by the distance x. As a pore wall we consider here the montmorillonite layer whose structure is known.25,26 The interaction of a molecule with this layer is approximated by a sum of interactions with four oxygen lattice planes parallel to the surface. For the potential of interaction with each plane we use the Lennard-Jones (LJ) potential integrated over two dimensions of the plane27 and we obtain
{ ()
us(z) ) 2πgsσgs2
2F1 σgs 5
z
10
∑ i)1
( )} σgs
4
-
Fi
z + di
4
(7)
where gs and σgs are the LJ potential parameters, Fi is the density, and di is the distance from the surface atoms nuclei of the ith oxygen plane. The adsorbate interactions (21) De Boor, C. A Practical Guide to Splines; Springer-Verlag: New York, 1978. (22) Everett, D. H.; Powl, J. C. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619. (23) Jagiełło, J.; Schwarz, J. A. J. Colloid Interface Sci. 1992, 154, 225. (24) Jagiełło, J.; Schwarz, J. A. Langmuir 1993, 9, 2513. (25) Grim, R. E. Clay Mineralogy; McGraw-Hill: New York, 1968. (26) Beutelspacher, H.; Van Der Marel, H. W. Atlas of Electron Microscopy of Clay Minerals and their Admixtures; Elsevier: Amsterdam, 1968; p 42. (27) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, 1974.
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Table 1. Parameters of the Effective Lennard-Jones Potential for the Molecule/Oxygen Ion Interactions set
molecule
/k (K)
σ (Å)
1 1 2 2
Ar SF6 Ar SF6
226.1 205.3 160.0 164.4
3.07 4.12 3.25 4.30
Table 2. Structural Parameters Obtained from X-ray Diffraction and Sorption of Nitrogen sample
d001 (Å)
interlayer spacing (Å)
SN2 (m2/g)
Vmic (cm3/g)
W W-A W-A(673) W-A(873)
12.4 18.4 17.6 16.0
5.9 11.9 11.1 9.5
30 350 330 309
0.126 0.113 0.107
with Si and Al atoms are not included. It is a common assumption28,29 to neglect the contribution of these atoms to the energy of dispersive interactions. This assumption is justified by the fact that these atoms are screened by oxygens ions and because their polarizabilities are very small.29 The LJ potential parameters describing interactions between adsorbate molecules and oxygen ions (SF6/O) were derived from the parameters of the effective LJ potential for Ar/O discussed by Bakaev and Steele.30 The values were calculated according to the following combining rules27
σAB )
(σAAσBB)3 σAA + σBB and AB ) xAABB 2 σ 6
Figure 1. X-ray diffraction patterns.
(8)
AB
using the following values of the gas-phase parameters: /k ) 119.8 K and σ ) 3.4 Å for Ar/Ar and /k ) 200.9 K and σ ) 5.51 Å for SF6/SF6.31 The resulting values of the LJ parameters for SF6/O based on the two sets of parameters for Ar/O discussed in ref 30 are presented in Table 1 together with the original ones. The first set of Ar/O parameters describes the effective LJ potential of Ar interaction with oxygen ions in zeolites32 while the second set was suggested30,33 to describe that interaction in the case of oxides such as TiO2. Results and Discussion The results of X-ray diffraction analysis are collected in Table 2. As expected, the intercalation with hydroxyaluminum polycations caused a significant increase in the interlayer distance compared to the initial form of the material.1,2 The d001 parameter of the intercalated sample, W-A, reaches 18.4 Å and then decreases for heat-treated samples. It is well-known that heat treatment of pillared clays results in the decrease of the d001 parameter due to the dehydration and dehydroxylation of pillars.1-4,9,17 Nevertheless, the bentonite intercalated with hydroxyaluminum pillars remains thermally stable until 873 K.2 Although heat treatment causes gradual broadening of the d001 pattern, relatively sharp peaks were obtained even after calcination at high temperature (Figure 1). (28) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieves; Academic Press: London, 1978. (29) Bezus, A. G.; Kiselev, A. V.; Lopatkin, A. A.; Du, P. Q. J. Chem. Soc., Faraday Trans. 1978, 74, 367. (30) Bakaev, V. A.; Steele, W. A. Langmuir 1992, 8, 1372. (31) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964. (32) Bakaev, V. A.; Smirnova, L. F. Izv. Akad. Nauk, Ser. Khim. 1978, 284. (33) Bakaev, V. A.; Steele, W. A. Langmuir 1992, 8, 1379.
Figure 2. Nitrogen adsorption isotherms.
From the results in Table 2 it is seen that the most pronounced changes in the structure of the intercalated mineral occur after heating at 873 K. At this temperature the process of dehydroxylation of hydroxyaluminum pillars is completed17 and the well-defined Al13 Keggin polycation is transformed into the oxide-like form of Al2O3.1 These changes are also reflected in the X-ray diffraction pattern; W-A(873) reveals a more broadened peak when compared to the initial and W-A(673) samples. In Table 2 we also report values of the interlayer space calculated by subtraction of the thickness of silicate layers (6.5 Å26) from d001 values. We assume this thickness to be constant for all samples. The values of the interlayer space represent the distance between the centers of the surface oxygen atoms of the opposite layers. Changes in the geometrical structure of materials can also be monitored by the parameters obtained from the measured nitrogen adsorption isotherms presented in Figure 2. From these isotherms we calculate the surface areas, SN2, (Langmuir equation) and micropore volumes, Vmic (DR equation), reported in Table 2. Results show that the sorption capacity slightly decreases with the increasing temperature of heat treatment. The same trend of a declining sorption capacity versus heat treatment temperature is shown by the SF6 adsorption isotherms presented in Figure 3. The SF6 isotherms
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Langmuir, Vol. 13, No. 5, 1997 1013
Figure 3. Adsorption isotherms of SF6.
Figure 4. Adsorption isotherms of SF6 for the W-A sample; solid lines, SAIEUS analysis; dotted lines fit by eq 10.
are more complex in shape compared to the nitrogen ones; they have two inflection points indicating a certain complexity during the adsorption process. We investigate each adsorption system in the following way. First we analyze the SF6 isotherm measured at the lowest temperature since that isotherm covers the broadest range of amount adsorbed and contains maximum information about the system. We fit eq 1 to this isotherm using the previously described SAIEUS procedure. The value of the lateral interaction parameter ω in eq 3 is estimated according to House and Jaycock34 as 1/4 of the heat of adsorbate liquefaction which gives for SF6 ω ) 5.85 kJ/mol.35 It is important to note that the value of the pre-exponential factor K in eq 3 is not known a priori; however, some estimates exist.36 In order to obtain K from the data, it is necessary to use isotherms measured at different temperatures because otherwise K and energy q in eq 3 are grouped together and it is impossible to evaluate separately the energy distribution and the K value. The factor K is weakly temperature dependent and for the localized adsorption model is given by36,27
K ) K0T-1/2
(9)
where K0 is a temperature-independent constant related to the force constant of vibration of the adsorbed molecule. We initially put for K0 an arbitrary value, K0 ) 1, and calculate the AED using the SAIEUS procedure. The resulting AED is shifted by a certain unknown value ∆q compared to the true distribution. Using this result, we calculate K0 and ∆q by fitting eq 1 to all three isotherms measured at different temperatures and thus we obtain the true energy scale for the AED. An example of such a fit for the W-A sample is presented in Figure 4. The resulting AEDs for all samples are presented in Figure 5. In each case the AED consists of two well-separated narrow peaks whose average adsorption energies qj 1 and q j 2 are reported in Table 3. In this table we also report the fractional contribution, x1, of the main peak to the total number of adsorption sites, v0. The last column of Table 3 gives the root mean square error of fit, δ. The fact that the AEDs obtained from SAIEUS analysis are represented by two distinct narrow peaks validates investigation of this adsorption systems in terms of a (34) House, W. A.; Jaycock, M. J. Colloid Polym. Sci. 1978, 256, 52. (35) Handbook of Chemistry and Physics, 53rd ed.; Weast, R. C., Ed.; CRC: Cleveland, OH, 1972. (36) Jaroniec, M.; Sokołowski, S.; Rudzin´ski, W. Z. Phys. Chem. (Leipzig) 1977, 258, 818.
Figure 5. Adsorption energy distributions. Table 3. Results of the SAIEUS Analyses sample W-A W-A(673) W-A(873)
v0 q j1 qj 2 (mmol/g) (kJ/mol) (kJ/mol) 1.27 1.18 1.00
24.5 22.9 21.0
31.8 30.9 28.6
x1 0.81 0.88 0.81
K0 δ (109 Torr) (mmol/g) 1.19 0.724 0.385
0.004 0.003 0.003
discrete AED distribution with two adsorption energies, q1 and q2. We obtain the following adsorption equation
v(p,T) ) v0{x1 θ(p,T,q1) + (1 - x1) θ(p,T,q2)}
(10)
where θ has the same meaning as in eq 3. The numerical results of fitting this equation to our experimental data are given in Table 4. In Figure 4 the isotherms obtained from this equation are compared with the experimental data and with the results obtained from SAIEUS for the W-A sample. Comparison of the results presented in Tables 3 and 4 demonstrates that both calculation methods give similar results, which implies that in the case of this adsorption system a continuous and discrete representation of the AED are virtually equivalent. The advantage of using eq 10 compared to the SAIEUS analysis is that we can evaluate all unknown parameters by a single fitting procedure; however, it can only be done in such special cases when the distribution is effectively discrete. It was of particular interest to obtain the best fit estimate of the ω parameter and compare its value with the estimate34 used in the SAIEUS analysis. We find that the maximum discrepancy between these two estimates is less than 15% (Table 4) and moreover that it has no significant effect on the calculated AEDs.
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Table 4. Results of Fitting of Equation 10 to the Experimental Data sample
v0 (mmol/g)
q1 (kJ/mol)
q2 (kJ/mol)
x1
K0 (109 Torr)
ω (kJ/mol)
δ (mmol/g)
W-A W-A(673) W-A(873)
1.27 1.15 0.97
24.8 22.2 20.5
32.1 30.1 28.3
0.81 0.84 0.78
1.31 0.655 0.359
5.8 6.7 6.4
0.003 0.002 0.002
Figure 6. Isosteric heats of adsorption of SF6 derived from eq 1 (solid lines) and from eq 10 (dotted lines).
Agreement between the continuous and discrete models is also seen in the isosteric heats of adsorption, Qst (Figure 6), calculated using eq 1 and 10 in conjunction with the Clausius-Clapeyron equation. The variation of Qst versus amount adsorbed, v, is often used to illustrate adsorption energetics without assuming any detailed adsorption model. We view the Qst plots in terms of the consistency with our assumptions and with AEDs results. We observe that the average Qst and AED values follow the same trend. All Qst plots have similar shape showing a minimum. The initial high Qst values are related to the adsorption on the highest energy sites described by the second peak of the AEDs. The decrease in Qst is related to the growing contribution of lower energy sites in the adsorption process whereas the subsequent increasing part of the plot is due to the growing contribution of the interaction energy between the molecules adsorbed on these sites. We now discuss the relationship between the observed adsorption energetics described by AEDs and the pore structure of the pillared clays. In our approach the adsorption energy is defined by the well depth of the gassolid interaction potential of a molecule adsorbed in a pore. Using eqs 6 and 7 describing the adsorption potential up in the pores of model pillared clays, we numerically evaluate the potential depth, up*, and thus adsorption energy, q, as a function of pore size x. The parameters Fi and di in eq 7 are derived according to the structure of the montmorillonite layer.26 For the distances, di, of the oxygen planes from the surface we take the following values: 0, 2.1, 4.4, 6.5 Å. We consider two values for the two-dimensional densities, Fi, of oxygen planes: F1 ) 0.133 atom/Å2 in the case of the original montmorillonite layer and F2 ) 0.11 atom/Å2 for the dehydroxylated layer. The latter value was obtained assuming that from each oxygen plane in a unit cell one oxygen ion was removed due to the dehydroxylation. In Figure 7 we present the variations of the adsorption energy versus pore size calculated for both sets of LJ parameters from Table 1 and for both values of F. It is seen that the potential described by the LJ parameters of set 2 predicts lower adsorption energies compared to those obtained from set 1. We also note that lower F leads to the lower q. In the calculations of PSDs for the initial pillared clay, W-A, and for the heat-treated sample, W-A(873), the densities F1 and F2 were used, respectively.
Figure 7. Variations of adsorption energy (depth of potential) as a function of pore width for both sets of the LJ potential parameters (Table 1) and different lattice densities, F1 and F2.
Figure 8. Pore size distributions calculated using F1 for the W-A sample for F2 for the W-A(873) sample.
The resulting PSDs are bimodal (Figure 8) since they were obtained from bimodal AEDs using eq 5. This result seems to be in contradiction with the well-defined structure of pillared clays for which we expect uniform pore sizes as, for example, determined by XRD. The position of the main peak for the W-A sample calculated from set 1 of the LJ parameters fits perfectly the interlayer spacing determined by XRD (Table 2). Using the second set of parameters leads to a shift of this peak by about 1 Å to smaller pore sizes, but is still in good agreement with the XRD results. The second smaller peak which appears for all PSDs in the range of 9-10 Å is derived from the AED peak representing the high-energy sites that contribute to about 20% in the total number of sites (Tables 3 and 4). We propose that these adsorption sites are located in the vicinity of pillars and thus their adsorption energy is enhanced due to the fact that the molecule adsorbed on these sites can interact with both the pillar and the pore. This concept is supported by the results of Grand Canonical Monte Carlo simulations of adsorption of simple gases in model pillared clays37 which have shown that gas atoms are preferably adsorbed in the corners between the pillars and the pore walls. The AED is less model dependent than the PSD and the calculated PSD represents the
Heterogeneity of Pillared Clays
distribution of pores having an assumed model structure, i.e., an ideal slitlike geometry which neglects interactions with pillars. As a consequence of this assumption, although pores are uniform in width, a second peak in the PSD corresponding to high-energy sites is obtained. This is an example of an artifact which can be obtained with inaccurate model assumptions. Another important factor, besides pore geometry, which plays a role in the calculation of pore width is the atomic structure of the solid. As shown in Figure 7, even slight changes in the number of oxygen atoms in the lattice of the mineral layer may considerably modify the adsorption potential. Consequently, taking incorrect lattice parameters leads to erroneous results. For example, if in the calculation of pore size for the W-A(873) sample we took one of the curves from Figure 7 with F1, we would obtain an unacceptably high value for x corresponding to 21 kJ/ mol of the main energy peak, whereas using F2 we obtain a smaller x than that for the W-A sample which is consistent with the XRD results. Our choice of the F2 value is somewhat arbitrary because we do not know exactly how many and from which lattice positions the (37) Cracknell, R.; Koh, C. A.; Thompson, S. M.; Gubbins, K. E. In Materials Research Society Proceedings; Drake, J. M., Klafter, J., Kopelman, R., Awschalom, D. D., Eds.; MRS: Pittsburgh, PA, 1993; Vol. 290, p 135.
Langmuir, Vol. 13, No. 5, 1997 1015
oxygen atoms are removed during the dehydroxylation. Although we obtain a decrease in pore size for the heattreated sample, it still does not fit the result of XRD; the difference is 1 or 1.5 Å. This discrepancy, besides the choice of F, may be due to our assumption that the montmorillonite layer does not shrink after heat treatment. Conclusion We find that physical adsorption of SF6 at near ambient temperatures is a useful and sensitive method to study the structure of pillared clays. The analysis of adsorption data provides information about adsorption energies which are related to the structural properties of the mineral. The overall consistency between the results obtained from the analyses of SF6 adsorption data for pillared clays using a slitlike pore model and XRD analysis is satisfactory. The discrepancies observed may be due to several factors such as uncertainty of the parameters of the LJ potential or the simplified method of calculation of the gas-solid interaction energy. Further systematic studies of this type of adsorption system may be used to establish reliable parameters describing solid structure and gassolid interaction potentials. LA951040X
